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Module[{nn=300, ono}, Range[nn]]; Union[Select[ Total/@ Tuples[ono, 2], MemberQ[ono, #]&]]] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Oct 26 2019 *)
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B. D. Swan, <a href="/A136346/b136346.txt">Table of n, a(n) for n = 01..1800</a>
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For sums of two positive octagonal numbers, see: A136345. This is to octagonal numbers A000567 as A089982 is to triangular numbers A000217 and , as A009000 is to squares A000290 and , as A136117 are is to pentagonal numbers A000326) and , as A133215 is to hexagonal numbers A000384 , and as A117104 is to heptagonal numbers A000566. If Oc(a) + Oc(b) = Oc(c) then a(3a-2) + b(3b+2) = c(3c+2), so solving the quadrataic quadratic equations for c we have (when an integer): c = (2 + SQRTsqrt(4 + 36a^2 + 36b^2 - 24a - 24b))/6.
B. D. Swan, <a href="/A136346/b136346.txt">Table of n, a(n) for n = 0,...,1800</a>
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_Jonathan Vos Post (jvospost3(AT)gmail.com), _, Dec 25 2007
B. D. Swan, <a href="/A136346/b136346.txt">Table of n, a(n) for n=0,...,1800</a>
easy,nonn,new